6.X2

A carcinogenicity study was conducted to examine the tumor potential of a drug 
scheduled for initial testing in humans. A total of 300 rats were studied for a 
6-month period. At the beginning of the study, 100 rats were randomly assigned 
to the control group, 100 to the low-dose group, and 100 to the high dose group. 
On each day, rats in the control group received an injection of a saline solution, 
wheras those in the drug groups received an injection of the solution plus drug. 
The sample data are shown in the table below.

          Group
         ------------------------
#Tumors  Control LowDose HighDose
=======  ------------------------
1+       10      14      19
None     90      86      81

a) Write out the hypotheses being tested symbolically in terms of p_i AND in words 
regarding independence.
b) Conduct a test of whether there is a significant difference in the proportion of 
rats having tumors for the three treatment groups at alpha=0.05.
c) Compute an odds ratio (OR) and state an interpretation for the control vs. low dose 
group (i.e., ignore the High dose group for calculating this OR). 
d) Compute a 95% CI for the OR above and state an interpretation.

Note: 
----
*I encourage you to use R for computations, but be sure that you can do them by hand 
as well. 
*Doing part (b) in R will require 3 entries in your 'x' & 'n' vectors 
[e.g., x=c(10,14,19)]. See the "Tests for 2 proportions & chi-square" link on the class 
software page.